questionable squares: a dialogue which explores questions, questioning, and defining
by Kye Nelson



One day when Big Lady was reading Meno, she got to the part that goes like this:

Soc. Tell me, boy, do you know that a figure like this is a square?

Boy. I do.

Soc. And you know that a square figure has these four lines equal?

Boy. Certainly.

Soc. And these lines which I have drawn through the middle of the square are also equal?

and she started wondering, "what would happen if Little Kid were asked questions like these?" And then she asked herself "how could you ask Little Kid questions that would let you get somewhere you wanted to go, without getting in the way of Little Kid's own questions?" Finally she thought she would go see if Little Kid would help her figure it out, and they had this conversation:


Big Lady: Did you know that a figure like this is called a square?

Little Kid: Yep. I know that's a square. But how come you called it a figure?

Big Lady: Well the real answer is I got the question out of a book and that's how they said it. If I asked you my own way I would have said 'did you know that this is a square?' That book keeps on talking about figures, and I'll bet we can figure out why they called it a figure. But that's a lot more complicated than what I was going to do. I wanted to explore about squares with you.

Little Kid: What about squares?

Big Lady: About when they get bigger. Can I ask you more of the book questions and see what happens?

Little Kid: Okay.

Big Lady: So did you know that a square figure has these four lines equal?

Little Kid: What's equal?

Big Lady: All the same.

Little Kid: But they're not all the same. These ones go up and down, and these go back and forth.

Big Lady: You're right. The book didn't ask the question well. Instead we could say 'did you know that all four sides of a square are the same length?' Does that make sense?

Little Kid: How do you know they are?

Big Lady: Because if they weren't, then it wouldn't be a square. That's how you make a square. You have to make it with all four sides exactly the same length.

Little Kid: How do you get them the same?

Big Lady: One way is to draw them with a ruler, like this. [draws a square]

Little Kid: But what if you got one side just a little tiny bit longer than the other ones? So you couldn't tell. Would it be a square or not?

Big Lady: It wouldn't be, because to really be a square they have to be exactly the same. But we would still call it a square.

Little Kid: How come we would call it one if it wasn't one? That would just mix people up. We ought to call it an almost-square.

Big Lady: Then we would have to call everything that we draw to be a square an almost-square, because there isn't any way to make them exactly the same length. We know that if they are drawn they are an almost-square, so we don't have to say the almost.

Little Kid: But people might forget about the almost if you leave it out. And you know what? If you can't make them the same, then there aren't any squares.

Big Lady: Maybe you're right. But could we pretend that there are squares so we can play with the book questions some more.

Little Kid: Okay.

Big Lady: So the next one says 'And these lines which I have drawn through the middle of the square are also equal?' So let's draw those lines in.

Little Kid: How do you know where the middle is?

And at this point Big Lady suddenly discovered that she was very tired and had to stop. But Little Kid wasn't tired at all.

This material © 2000 by Kye Nelson. All rights reserved.

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